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A290741
Orbit of word "2" under the 3-shift tag system over the alphabet {1,2} defined in the Comments.
4
2, 21222, 221221222, 2212221221222, 22212212221221222, 122122212212221221222, 1222122122212212222112, 21221222122122221122112, 212221221222211221121221222, 2212212222112211212212221221222, 22122221122112122122212212221221222, 222211221121221222122122212212221221222
OFFSET
1,1
COMMENTS
This tag system maps a word w over {1,2} to w', where if w begins with 1, w' is obtained by appending 2112 to w and deleting the first three letters, or if w begins with 2, w' is obtained by appending 1221222 to w and deleting the first three letters.
This is a 3-shift version of a 5-shift tag system studied in [De Mol, p. 307] (cf. A293945).
MAPLE
with(StringTools);
f1:=proc(w) local L, t2, t1, ws, w2;
t1:="2112"; t2:="1221222"; ws:=convert(w, string);
if ws[1]="1" then w2:=Join([ws, t1], ""); else w2:=Join([ws, t2], ""); fi;
L:=length(w2); if L <= 3 then return(-1); fi;
w2[4..L]; end;
# and apply f1 repeatedly to "2"
PROG
(Python)
from itertools import islice
def agen(w="2"):
while True:
yield int(w)
w += ("2112" if w[0] == "1" else "1221222")
w = w[3:]
print(list(islice(agen(), 12))) # Michael S. Branicky, Mar 15 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 11 2017
EXTENSIONS
Definition corrected by N. J. A. Sloane, Oct 23 2017 (this is not De Mol's 5-shift tag system, which is described in A293945).
STATUS
approved